LCM of 24 and 54 is 216. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 24 and 54 is the smallest number among all common multiples of 24 and 54. The first few multiples of 24 and 54 are (24, 48, 72, 96, 120, 144, 168, . . . ) and (54, 108, 162, 216, 270, . . . ) respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 24 and 54?
The answer to this question is 216. The LCM of 24 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 54, is the smallest positive integer 216 which is divisible by both 24 and 54 with no remainder.
How to Find LCM of 24 and 54?
LCM of 24 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 54 Using Prime Factorisation Method
The prime factorisation of 24 and 54, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31 and
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (24, 54) = 216
LCM of 24 and 54 Using Division Method
We’ll divide the numbers (24, 54) by their prime factors to get the LCM of 24 and 54 using the division method (preferably common). The LCM of 24 and 54 is calculated by multiplying these divisors.
| 2 | 24 | 54 |
| 2 | 12 | 27 |
| 2 | 6 | 27 |
| 3 | 3 | 27 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 54) = 216
LCM of 24 and 54 Using Listing the Multiples
To calculate the LCM of 24 and 54 by listing out the common multiples, list the multiples as shown below
| Multiples of 24 | Multiples of 54 |
| 24 | 54 |
| 48 | 108 |
| 72 | 162 |
| 96 | 216 |
| 120 | 270 |
| 144 | 324 |
| 168 | – |
| 192 | – |
| 216 | – |
The smallest common multiple of 24 and 54 is 216.
Therefore LCM (24, 54) = 216
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LCM of 24 and 54 Solved Example
Question: The product of two numbers is 1296. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 1296
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1296/6
Therefore, the LCM is 216.
The probable combination for the given case is LCM(24, 54) = 216.
Frequently Asked Questions on LCM of 24 and 54
What is the LCM of 24 and 54?
List the methods used to find the LCM of 24 and 54.
If the LCM of 54 and 24 is 216, Find its GCF.
Since the LCM of 54 and 24 = 216
⇒ 216 × GCF(54, 24) = 1296
Therefore, the GCF (greatest common factor) = 1296/216 = 6.
What is the Least Perfect Square Divisible by 24 and 54?
LCM of 24 and 54 = 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 24 and 54 = LCM(24, 54) × 2 × 3 = 1296 [Square root of 1296 = √1296 = ±36] Therefore, 1296 is the required number.
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